120 is a pretty acceptable temperature. And yes, both themostats should be at the same temperature. They used to be set at 150 and the recomendation was changed to 120 for conservation reasons. Of course now there is a whole new theory in some regions (required in my region)...they find that bacteria can grow in 120 degrees so they are requiring the tanks to be set at 180 to kill bacteria and then the outgoing water be mixed with cold water so someone doesn't get scalded:-) Maybe someone can enlighten us on this subject. But for your purposes (and mine) I would say 120 is good.

It's prohibited for one. And for two, to actually run an electric tankless will require most of the power that you currently have in your panel. 125-200 amps are needed. If you live in a cold climate, electrical is not really doable at all because of the incoming winter water temperature. Gas tankless is much easier to retrofit, and even it may require new gas service for the home.

Is there a faucet or fixture close to the water heater? Is it flowing backwards from the hot side from a water fixture? Is there a shut off valve for the hot side? Is there a recirculating system? Also, the water heater shouldnt be on if it is not filled up.

I am just researching which electric water heater to go with. Theoretical payback is dependent on equipment. If we compare 50 Gallon Rheem Platinum vs Geospring: Assuming optimum tested conditions for simplicity of comparison. Cost of operation is $555 vs $182 per year. Install cost I am not sure assuming similar. Then $555 - $182 = $373 savings per year. Cost of equipment is $568 vs $1200. $1200 - $568 = $632. Number of years to recover extra cost is $632 / $373 = 1.69 years. This not assuming any rebates. In some areas they are giving $750 rebate from utility company, in which case break even is when you get rebate immediately. Is that what you are looking for? Not decided on plumber or DIY. Seems easy to hook up on your own using flexible hot water connectors such as sharkbite, etc. , especially if you are replacing with similar electric water heater. Little taller and have to make sure you have required space. Also have to hook up pump if you don't have drain which might be little more install cost. Why?